问题求解

For the generalized boundary value problem a complete set of boundary integral equations and relevant numerical scheme are established.

利用 Hankel 变换导出了弹性地基上薄板弯曲问题的基本解，此基本解对三种常用地基模型具有统一的表达形式，针对近年提出的广义边值问题，建立了统一的边界积分方程和边界元求解格式。

Based on analyzing the problems,we propose an evolutionary algorithm by using niches technology and multi-parent-crossover technology to experiment on complex multimodal function optimization with samples.

在分析了简单遗传算法求解带约束的多峰值函数优化中存在的问题的基础上，提出了利用小生境技术和多父体杂交的演化算法，对复杂的多峰值函数优化问题进行了测试，证实该算法能够快速求出多峰函数的所有全局最优解，而且搜索效率高，达到了令人满意的效果。

Because of their intrinsic characteristics of hard computability, they cannot be solved accurately by efficient algorithms up to now. Since these problems have many applications in real situations, it is quite important to find some applicable algorithms.

由于难计算是这类问题的固有性质，因此它们目前尚无法用有效算法精确求解，但这些问题在现实领域中有着许多广泛的应用，因而寻找其实际而有效的算法就显得颇为重要了。

Combining the specific knowledge of computational Model-minimum Error Correction for the haplotype reconstruction problem,an improved particle swarm optimization was proposed to solve the haplotype reconstruction problem.

结合单体型装配问题的计算模型—最少错误纠正模型的特定知识，提出了一种求解单体型装配问题的改进粒子群算法。

Method\ Percolation of multiple-hole horizontal well is exchanged to radial percolation by applying conformal transformation theory and local percolation restriction .

应用保角变换原理和局部渗流阻力的概念，将多分枝水平井渗流问题转变为平面径向渗流问题，从而简化了求解过程。

In chapter 2,by referring to the algorithm in paper[7],we present a class of conjugate gradient methods connected with Hestenes-Stiefel Algorithm.

在第一章中，我们首先简要的介绍了最优化问题的提出以及判断最优解常用的最优性条件；回顾了求解无约束优化问题常用的几类导数下降类算法。

A boundary identification problem, i.e., inverse geometry problem of two-dimensional heat conduction was solved by using boundary element method and conjugate gradient method-based inverse algorithm.

采用基于边界元法和共轭梯度法的反演算法求解二维导热边界识别问题，即几何反问题。

Using level-set method, mathematical representation for contimuum structures is proposed by means of the vector of level-set, and the general structure topology optimization can be expressed by a constrained functional minimization problem of a set of level set functions.

其次利用水平集方法将一般拓扑优化问题描述为一组水平集函数的约束泛函极小化问题，应用敏度分析，给出了此泛函极小化数值迭代求解公式，即水平集演化方程。

By establishing MINLP model, the computation of phase equilibrium is transformed into a constrained two-level minimization problem. On the inner level, equilibrium composition is computed; On the outer level, the optimum phase combination configuration is searched for. The whole solving process is achieved by Genetic Algorithm.

通过建立MINLP模型，将相平衡计算问题转化为有约束的双层最优化问题，内层用来计算给定相组合结构下的平衡组成，外层则是搜索最优的相组合结构，整个求解过程通过遗传算法来实现。

According to the low speed of constringency and high complexity of training methods in large scale training, particle swarm algorithm is brought forward to solve the problem.

针对在大规模训练中算法收敛速度慢、复杂程度高等问题，提出用粒子群算法求解其中的二次规划问题的思想。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。